Determinants of the Pace of Global Innovation in Energy Technologies

Understanding the factors driving innovation in energy technologies is of critical importance to mitigating climate change and addressing other energy-related global challenges. Low levels of innovation, measured in terms of energy patent filings, were noted in the 1980s and 90s as an issue of concern and were attributed to limited investment in public and private research and development (R&D). Here we build a comprehensive global database of energy patents covering the period 1970–2009, which is unique in its temporal and geographical scope. Analysis of the data reveals a recent, marked departure from historical trends. A sharp increase in rates of patenting has occurred over the last decade, particularly in renewable technologies, despite continued low levels of R&D funding. To solve the puzzle of fast innovation despite modest R&D increases, we develop a model that explains the nonlinear response observed in the empirical data of technological innovation to various types of investment. The model reveals a regular relationship between patents, R&D funding, and growing markets across technologies, and accurately predicts patenting rates at different stages of technological maturity and market development. We show quantitatively how growing markets have formed a vital complement to public R&D in driving innovative activity. These two forms of investment have each leveraged the effect of the other in driving patenting trends over long periods of time.

Solar: (photovoltaic or "photo voltaic" or (solar and cell)) and (electric* or energy or power or generat* or turbine or vehicle) Hydroelectric: ("hydro electric" or "hydro power" or hydroelectric or hydropower) and (electric* or energy or power or generat* or turbine or vehicle) Geothermal: (geothermal or "geo thermal") and (electric* or energy or power or generat* or turbine or vehicle) Wind: "Wind" and (electric* or energy or power or turbine) and (generat*) Biofuels: ("bio fuel" or "bio diesel" or biofuel or biodiesel) and (electric* or energy or power or generat* or turbine or vehicle) Nuclear fission: (nuclear fission) and (electric* or energy or power or generat* or turbine or vehicle) Nuclear fusion: (nuclear fusion) and (electric* or energy or power or generat* or turbine or vehicle) Individual technologies were then aggregated to form the classes of fossil fuel, renewable and nuclear technologies, and ultimately the set of patents in energy technology.
The breakdown of numbers of patents published by technology are given in Table S1 and their shares by nation are illustrated in Fig. 2C. Figures in the paper refer to patents published unless otherwise noted (e.g. in Figure 4, which is based on patent applications).

Data on Cumulative Production
Global production data for solar (photovoltaics) and wind was obtained from references (5)(6)(7). US coal electricity production data was obtained from reference (8). See Figures S8 and S10. These are the data used to populate the time series for C, as discussed below.

Derivation of production function for patents
We draw on the basic conceptual model of knowledge creation by Griliches (9), which relates patenting, P, to public R&D, R, and market size, C, via knowledge K (see Figure 3, main manuscript). We modify the conceptual model to capture the relationship between the proportional changes in variables, and express it as follows: which is eq. (2) in the main text, though there we do not show the component relating to Δ, as discussed below. We assume (and test against the data) that the coefficients α, β, δ are constants in time. Then we can integrate (S3) to obtain (S2) This is the form used below and in the main text in eq. (1) to estimate parameter values (where we absorb the Δ dependence in the other terms, see comments below) and verify that the ratios α, β are consistent with the hypothesis of their constancy. We also directly fit eq. (S1 and 2 in the main text) to the data.
A few comments on this derivation and its consequences are in order: 1) We have used cumulative quantities over time because the effects of knowledge production are nonlocal in time and accumulating. We find empirically that this is necessary to account for trends in the data. The treatment of these variables as cumulative quantities (stocks) is different from several commonly observed functions in the literature, such as the Cobb-Douglas production function, in that even if an input ceases to grow the cumulative base in that input will continue to enhance the value of new investment in the others. In our model the effects of market driven investment in knowledge creation today multiply the cumulative past R&D investment and vice-versa. This is because of the character of knowledge, which differs from other produced goods and services to which a Cobb-Douglas production function (with non-cumulative inputs) typically applies. In practice, past knowledge can become obsolete but the rate at which this happens is difficult to quantify.
2) We assume that the quantities R and C can be expressed at a single time lag relative to P, which is a particular (simplifying) case in the integration from Eq. (S1) to (S2). It is only in the case of wind technologies that we observe a tangible lag, where C lags patents by 3-4 years. This may reflect investments that are made ahead of large, planned wind installations. These assumptions can be relaxed but only at the cost of introducing contributions at more time points, thus more functional freedom in the fit, and potentially over-fitting of the data.
3) The quantity Δ is not observed but it could account, for example, for venture capital. However, we find that any systematic independent temporal trend that it may introduce in patterns of invention is at most very small. An independent factor driving patents would be expected to lead to a temporal variation in P 0 , which is not observed. This implies that its variation is either negligible or that it is strongly correlated, and can be expressed in terms of, temporal trends in C, and R, i.e.
In this case the measured exponents include an implicit contribution from variations in Δ as in € α →α + aδ, β →β + bδ . However, because we do not know a, b we can only assert that they must be approximately constant in time. Note, that in principle they can be negative, if the relative variation of Δ and the other variables were anti-correlated. 4) In the observed exponents α, β (absorbing the contributions discussed above) we see that α+β <1, which holds empirically in all cases estimated below.
5) The multiplicative effects of knowledge creation on technology improvement, market expansion and presumably increased profits, implies that (when examined in the opposite direction from the one written above) C ~ P 1/ β , where 1/β is larger than 1. This relationship shows increasing returns to scale in economic performance to knowledge creation (proxied by patents), as expected from general theoretical considerations. Once created, this virtuous cycle may lead to the self-sustaining improvement of a technology in tandem with its market expansion, as suggested in Figure 3.

Model regression and best-fit parameter estimates
In this section we fit equation 1 in the main text to the globally aggregated time series data for cumulative public research and development funding (R&D), production, and patents for solar, wind and coal. The results are shown in Figure 4 where we plot the natural logarithm of cumulative patent counts over time. To further verify these results with stationary time series, we also fit equation 2 in the main text to the data.

Solar
N logP 0 std error α std error β std error adj--R 2   Figure 4 of the main text. Other rows show the sensitivity of the parameter estimates fits to different time lags, t R for R&D and t C for production, measured in years. ('+1' means that patents precede C or R by one year.) The parameter estimates are significant in all cases, especially for the best fit, which has p values of 2e-16, 1.65e-09 and 8.48e-10 for log P 0 , α and β respectively.   Table S3A: Results of applying Eq. (1) in the main text to cumulative patents filed globally in wind technologies, cumulative global R&D funding and cumulative global production (in terms of turbine capacity). The highlighted row indicates the best-fit parameters used in Figure 4 of the main text. p-values for best fit parameters (highlighted) are 0.105, 7.84 e-5, 1.35 e-9, for log P 0 , α and β respectively.
Wind N α std error β std error adj--R 2 tR=0, tC=+4 22 0.48 0.13 0.29 0.06 0.10 Table S3B: Results of applying Eq. (2) in the main text to the first difference of the logs of cumulative wind patents, R&D funding and production (in terms of turbine capacity). These time series pass the Dickey-Fuller test of stationarity. The row shown is the best-fit time lag (which is consistent with that in Table S3A). Despite the lower value for the adjusted-R 2 as compared to the fit to Eq. (1), the parameter estimates are significant, with p values of 1.55e-3, and 1.01e-4, for α and β respectively.  Table S4A: Results of applying Eq. (1) in the main text to coal technologies. Production in this case refers to energy generation (rather than capacity). Patents, production and R&D investments are for the US only. The highlighted row indicates the best-fit parameters used in Figure 4 of the main text. p-values for best fit parameters (highlighted) are 1.67e-14, 1.74e-12, < 2e-16.

US coal N logP
US coal N α std error β std error adj--R 2 tR=--1, tC=0 32 0.29 0.01 0.68 0.08 0.949 Table S4B: Results of applying Eq. (2) in the main text to the first difference of the logs of cumulative US coal patents, R&D funding and energy generation. These time series pass the Dickey-Fuller test of stationarity. The row shown is the best-fit time lag (which is consistent with that in Table S4A). The parameter estimates are significant, with p values of 1.67e-23, and 1.74e-9, for α and β respectively.  Table S5A: Best fit parameters for solar technologies applying Eq. (1) from the main paper but including R&D only (not production). Note that the fits are worse than those of Table S2A, suggesting that market growth of the technology is an essential ingredient stimulating patents and knowledge creation.  Table S5B: Best fit parameters for solar technologies applying Eq. (2) from the main paper but including R&D only (not production). Note that the fits are worse than those of Table S2B, indicating the importance of market growth.     Table S7B: Best fit parameters for US coal applying Eq. (2) from the main paper including R&D only (not production). Note that the fits are worse than those of Table  S4B. Figure S1: Temporal trends for the fraction of all patents accounted for by energy technologies filed in the USA (USPTO). This fraction was computed using US patents granted (as reported elsewhere in this study) over the total number of US applications for all sectors, with a time lag of two years (the average time between application and granting a patent, sometimes referred to as the average pendency time). These trends indicate that energy patents are growing faster than overall patenting rates, which themselves have been increasing over time due to high growth rates in highly innovative sectors such as the semiconductor, computer technology, biotechnology, and medical technology industries. The data shows that the fractional high rates of energy patenting are mostly due to activity in renewable energy technologies.             The focus on the US is motivated by more limited knowledge spillover in the case of coal than solar and wind (higher installation and operating costs).